Đáp án:
$min_A=2\Leftrightarrow x=-1\\ min_B= -14 \Leftrightarrow x=\dfrac{3}{2}\\ min_C= -\dfrac{49}{4} \Leftrightarrow x=-\dfrac{5}{2}\\ max_D= 2 \Leftrightarrow x=\dfrac{1}{2}\\ max_E= 19 \Leftrightarrow x=-3\\ max_G=\dfrac{401}{4} \Leftrightarrow x=-\dfrac{7}{2}$
Giải thích các bước giải:
$A=x^2+2x+3\\ =x^2+2x+1+2\\ =(x+1)^2+2 \ge 2 \ \forall \ x$
Dấu "=" xảy ra $\Leftrightarrow x+1=0 \Leftrightarrow x=-1$
$B=4x^2-12x-5\\ =4x^2-12x+9-14\\ =4\left(x^2-3x+\dfrac{9}{4}\right)-14\\ =4\left(x-\dfrac{3}{2}\right)^2-14 \ge -14 \ \forall \ x$
Dấu "=" xảy ra $\Leftrightarrow x-\dfrac{3}{2}=0 \Leftrightarrow x=\dfrac{3}{2}$
$C= x^2+5x-6\\ =x^2+5x+\dfrac{25}{4}-\dfrac{49}{4}\\ =\left(x+\dfrac{5}{2}\right)^2-\dfrac{49}{4} \ge -\dfrac{49}{4} \ \forall \ x$
Dấu "=" xảy ra $\Leftrightarrow x+\dfrac{5}{2}=0 \Leftrightarrow x=-\dfrac{5}{2}$
$D=-4x^2+4x+1\\ =-4x^2+4x-1+2\\ =-(4x^2-4x+1)+2\\ =-(2x-1)^2+2 \le 2 \ \forall \ x$
Dấu "=" xảy ra $\Leftrightarrow 2x-1=0 \Leftrightarrow x=\dfrac{1}{2}$
$E=-x^2-6x+10\\ =-x^2-6x-9+19\\ =-(x^2+6x+9)+19\\ =-(x+3)^2+19 \le 19 \ \forall \ x$
Dấu "=" xảy ra $\Leftrightarrow x+3=0 \Leftrightarrow x=-3$
$G=-x^2-7x+88 \\ =-x^2-7x-\dfrac{49}{4}+\dfrac{401}{4}\\ =-\left(x^2+7x+\dfrac{49}{4}\right)+\dfrac{401}{4}\\ =-\left(x+\dfrac{7}{2}\right)^2+\dfrac{401}{4} \le \dfrac{401}{4} \ \forall \ x$
Dấu "=" xảy ra $\Leftrightarrow x+\dfrac{7}{2}=0 \Leftrightarrow x=-\dfrac{7}{2}$
